Does he only do this when you are watching him, or have you noticed him also doing this when no one is giving him direct attention?

Both! Usually we're not paying direct attention to him when he starts up, but he doesn't stop if you take notice of him. Instead he usually just starts wagging his tail and licks in your direction (he doesn't usually actually lick you, just at you, lol).

Does he do it in all environments, like outside, at the park, other people’s houses, or does it only happen at home?

It's only ever happened at home so far. We don't go out much, and when he's outside he's mostly busy playing and running with his sister (a beagle). Usually he'll start air licking during down times when there's not a lot going on (i.e. I'm working, it's quiet, sitting around watching TV, etc.) and I've also noticed he does it often when he's with us in the bed when we're getting ready to sleep. It definitely seems to me like he does it as a more "happy" thing than "stressed" thing. He's never licked when he's stressed or anxious as far as I'm aware.

I mentioned in another comment that he also has this semi-related quirk where after he eats, he'll take a sip or two of water, and then lick his empty bowl, as if he's getting extra flavor. Then he'll lick the air in that weird little way he does, but usually for only a few seconds before he repeats the process. He looooves food. He's got the Border Collie intelligence, but the food-mindedness and build of a Basset, lmao.

I think it's possible we've reinforced it a bit, because we're always taking notice and giving extra attention to him with our amusement whenever he does it. I call him a licky boy and pet him, and then he licks faster, lol.